## Annuity:

People are recommended to include an annuity in their retirement portfolio as an annuity can produce a series of payments during a specific period. In practice, annuity payments can be grown at a constant rate to beat the inflation.

Summary:

Bond account:

• Available fund = $150,000 • Annual deposit =$9,000
• Number of deposits = 10
• Annual interest rate (I1) = 7.5%

Stock account:

• Available fund = $450,000 • Annual interest rate (I2) = 11.5% Determine the value of the stock account after 10 years: {eq}Value_{stock} = \displaystyle Availabe\:fund_{stock}\times (1 + I2)^N {/eq} {eq}Value_{stock} = \displaystyle \$450,000\times (1 + 11.5\%)^{10} {/eq}

{eq}Value_{stock} = $1,336,476.07 {/eq} Determine the value of the bond account after 10 years: {eq}Value_{bond} = \displaystyle Available\:fund_{bond}\times (1 + I1)^N + \displaystyle Deposit\times \frac{(1 + I1)^N - 1}{I1} {/eq} {eq}Value_{bond} = \displaystyle \$150,000\times (1 + 7.5\%)^{10} + \displaystyle \$9,000\times \frac{(1 + 7.5\%)^{10} - 1}{7.5\%} {/eq} {eq}Value_{bond} =$309,154.73 + $127,323.79 {/eq} {eq}Value_{bond} =$436,478.52 {/eq}

Determine the total amount of money available after 10 years:

{eq}Total\:fund = Value_{stock} + Value_{bond} {/eq}

{eq}Total\:fund = $1,336,476.07 +$436,478.52 {/eq}

{eq}Total\:fund = $1,772,954.59 {/eq} Determine the annual withdrawal within 25 years: {eq}Withdrawal = \displaystyle \frac{Total\:fund}{\displaystyle\frac{1-(1 + I)^{-N}}{I}} {/eq} {eq}Withdrawal = \displaystyle \frac{\$1,772,954.59}{\displaystyle\frac{1-(1 + 6.75\%)^{-25}}{6.75\%}} {/eq}

{eq}Withdrawal = \$148,727.69 {/eq} The investor can withdraw an equal amount of$148,727.69 per year within 25 years after the retirement.